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One way to reduce the large degeneracy of the hyperspherical-harmonic basis for solving fewand many-body bound-state problems is to introduce an optimal basis truncation called the potentialharmonic (PH) basis. In this paper we introduce various potential-harmonic truncation schemes and assess their accuracies in predicting the energies of the helium and H ground states and the excited 2 'S level of the helium atom. We first find that the part of the PH basis that accounts for one-body correlations gives a better ground-state energy for He than Hartree-Fock (2.8790 a.u. versus 2.8617 for Hartree-Fock and 2.9037 exact). When an orthogonal complement is introduced to the basis to account for e-e correlations, we find that the error in the binding energy is 0.00025 a.u. , and 0.00015 a.u. for ground-state and excited helium, and 0.00035 a.u. for H . Furthermore, the PH truncation is about 99.9% accurate in accounting for contributions coming from large values of the global angular momentum. This PH scheme is also much more accurate than previous versions based on the Faddeev equations. The present results indicate that the PH truncation can render the hyperspherical-harmonic method useful for systems with X)3. PACS number(s): 31.15.+q

The quantum-mechanical second virial coefficients of Lennard-Jones 3He and 4He gases with the De Boer parameters have been obtained over the complete temperature range from near absolute zero to the classical region. A formalism separating the virial into direct (Boltzmann) and exchange (spin and quantum statistics) contributions has been employed. The calculation is based on phase shifts except at the very highest temperatures where a Wigner–Kirkwood method has been used. Examination of the exchange term shows in detail the rapid suppression of the statistical effects with rising temperature, their contribution dropping to less than 0.001 cm3 by 7°K (4He). Comparison of the high-temperature (Boltzmann) results with those obtained by a third-order Wigner–Kirkwood expansion shows excellent agreement down to about 50°K for 4He and 60°K for 3He. The Wigner–Kirkwood expansion is shown to be unsuitable for determining the behavior of the exchange terms. Finally, results are compared with the available experimental data.